Question: Which of the following numbers is a factor of 140? ${6,9,11,12,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $140$ by each of our answer choices. $140 \div 6 = 23\text{ R }2$ $140 \div 9 = 15\text{ R }5$ $140 \div 11 = 12\text{ R }8$ $140 \div 12 = 11\text{ R }8$ $140 \div 14 = 10$ The only answer choice that divides into $140$ with no remainder is $14$ $ 10$ $14$ $140$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $140$ $140 = 2\times2\times5\times7 14 = 2\times7$ Therefore the only factor of $140$ out of our choices is $14$. We can say that $140$ is divisible by $14$.